Animal navigation: the difficulty of moving in a straight line

In principle, there are two strategies for navigating a straight course. One is to use an external directional reference and continually reorienting with reference to it, while the other is to infer body rotations from internal sensory information only. We show here that, while the first strategy will enable an animal or mobile agent to move arbitrarily far away from its starting point, the second strategy will not do so, even after an infinite number of steps. Thus, an external directional reference—some form of compass—is indispensable for ensuring progress away from home. This limitation must place significant constraints on the evolution of biological navigation systems. Some specific examples are discussed. An important corollary arising from the analysis of compassless navigation is that the maximum expected displacement represents a robust measure of the straightness of a path.

[1]  G. Weiss,et al.  A descriptive theory of cell migration on surfaces. , 1974, Journal of theoretical biology.

[2]  K. Mardia.  Statistics of Directional Data , 1972 .

[3]  R. Wehner,et al.  The polarization-vision project: championing organismic biology , 1994 .

[4]  Stanley,et al.  Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight. , 1994, Physical review letters.

[5]  H. Stanley,et al.  Optimizing the success of random searches , 1999, Nature.

[6]  Ingemar J. Cox,et al.  Blanche-an experiment in guidance and navigation of an autonomous robot vehicle , 1991, IEEE Trans. Robotics Autom..

[7]  P. Day.  The Organisation of Learning , 1977 .

[8]  A S Etienne,et al.  Path integration in mammals and its interaction with visual landmarks. , 1996, The Journal of experimental biology.

[9]  J. Byers.  CORRELATED RANDOM WALK EQUATIONS OF ANIMAL DISPERSAL RESOLVED BY SIMULATION , 2001 .

[10]  Sebastian Thrun.  To Know or Not to Know: On the Utility of Models in Mobile Robotics , 1997 .

[11]  T. S. Collett,et al.  View-based navigation in Hymenoptera: multiple strategies of landmark guidance in the approach to a feeder , 1997, Journal of Comparative Physiology A.

[12]  Helmut Schwegler,et al.  Path integration — a network model , 1995, Biological Cybernetics.

[13]  R. Wehner.  Spatial organization of foraging behavior in individually searching desert ants, Cataglyphis (Sahara Desert) and Ocymyrmex (Namib Desert) , 1987 .

[14]  Shlesinger.  Comment on "Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight" , 1995, Physical review letters.

[15]  A. Etienne,et al.  Navigation through vector addition , 1998, Nature.

[16]  Zollikofer.  STEPPING PATTERNS IN ANTS - INFLUENCE OF BODY MORPHOLOGY , 1994, The Journal of experimental biology.

[17]  W. Wiltschko,et al.  Magnetic orientation and magnetoreception in birds and other animals , 2005, Journal of Comparative Physiology A.

[18]  Simon Benhamou,et al.  Spatial memory in large scale movements: Efficiency and limitation of the egocentric coding process , 1990 .

[19]  C. McCulloch,et al.  Analyzing Discrete Movement Data as a Correlated Random Walk , 1989 .

[20]  P. Görner,et al.  Homing Behavior and Orientation in the Funnel-Web Spider, Agelena labyrinthica Clerck , 1985 .

[21]  M. Rosenblatt.  Remarks on Some Nonparametric Estimates of a Density Function , 1956 .

[22]  B. Nahapetian.  Limit theorems and some applications in statistical physics , 1991 .

[23]  S. Benhamou,et al.  Spatial analysis of animals' movements using a correlated random walk model* , 1988 .

[24]  Horst Mittelstaedt,et al.  Homing by Path Integration , 1982 .

[25]  Friedrich G. Barth,et al.  Idiothetic orientation of a wandering spider: Compensation of detours and estimates of goal distance , 1982, Behavioral Ecology and Sociobiology.

[26]  P. Kareiva,et al.  Analyzing insect movement as a correlated random walk , 1983, Oecologia.

[27]  Rüdiger Wehner,et al.  Desert ants compensate for navigation uncertainty , 2005, Journal of Experimental Biology.

[28]  A. S. Edwards,et al.  Ontogeny of orientation flight in the honeybee revealed by harmonic radar , 2000, Nature.

[29]  Georg Hartmann,et al.  The ant's path integration system: a neural architecture , 1995, Biological Cybernetics.

[30]  H. Mittelstaedt,et al.  Homing by path integration in a mammal , 1980, Naturwissenschaften.

[31]  Lars Chittka,et al.  Navigation without vision: bumblebee orientation in complete darkness , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[32]  F. Barth,et al.  Neurobiology of Arachnids , 1985, Springer Berlin Heidelberg.

[33]  E. Batschelet.  Circular statistics in biology , 1981 .